Yi-Jing Xu's research while affiliated with John Tyler Community College and other places
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Publications (5)
The moduli algebra A(V) of a hypersurface singularity (V,0) is a finite-dimensional ℂ-algebra. In 1982, Mather and Yau proved that two germs of complex-analytic hypersurfaces of the same dimension with isolated singularities are biholomorphically equivalent if and only if their moduli algebras are isomorphic. It is a natural question to ask for a n...
Citations
... Proposition III.1 (Ref.31, Proposition 2.6). ...
... First, we recall some useful lemmas. [7]). Let f be a weighted homogeneous polynomial with isolated singularity in x 1 , . . . ...
... Before continuing, let's briefly sketch the state of the art of Durfee's conjecture 1.2. In the early 90s, some special cases were proven by different mathematicians: for ( , 0) of multiplicity 2 Tomari's Theorem 3.1 proves a stronger inequality 8 < , for multiplicity 3 Ashikaga [3] proves the inequality 6 ≤ − 2, for quasi-homogeneous singularities Xu and Yau [42] prove the inequality 6 ≤ − mult( , 0) + 1. At the end of the 90s, the inequality 6 ≤ is proven for the following families of surface singularities: Némethi [28,29] for suspension type singularities { ( , ) + = 0 } and Melle-Hernández [25] for absolutely isolated singularities. ...
... The hunt for a good, simple estimate of q(α 1 , ..., α n ) and p(α 1 , ..., α n ) led to several results [7,8,9,15,17,18,19], finally put together in the GLY Conjeture, named after its authors Granville, Lin and Yau. ...
... The hunt for a good, simple estimate of q(α 1 , ..., α n ) and p(α 1 , ..., α n ) led to several results [7,8,9,15,17,18,19], finally put together in the GLY Conjeture, named after its authors Granville, Lin and Yau. ...
